This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A289916 #11 Jul 20 2017 06:12:45
%S A289916 1,3,5,8,13,22,39,69,120,206,353,607,1046,1803,3106,5348,9208,15856,
%T A289916 27306,47025,80982,139457,240155,413566,712196,1226463,2112073,
%U A289916 3637166,6263503,10786276,18574872,31987488,55085136,94861220,163358969,281317834,484452887
%N A289916 Coefficients of 1/(Sum_{k>=0} round((k+1)*r)(-x)^k), where r = 9/7.
%C A289916 Conjecture: the sequence is strictly increasing.
%H A289916 Colin Barker, <a href="/A289916/b289916.txt">Table of n, a(n) for n = 0..1000</a>
%H A289916 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,1,-1,2,-1).
%F A289916 G.f.: 1/(Sum_{k>=0} round((k+1)*r)(-x)^k), where r = 9/7.
%F A289916 From _Colin Barker_, Jul 19 2017: (Start)
%F A289916 G.f.: (1+x)^2*(1-x+x^2-x^3+x^4-x^5+x^6) / ((1-x+x^2)*(1-x-x^2-x^3+x^4)).
%F A289916 a(n) = 2*a(n-1) - a(n-2) + a(n-3) - a(n-4) + 2*a(n-5) - a(n-6) for n>5.
%F A289916 (End)
%t A289916 z = 2000; r = 9/7;
%t A289916 u = CoefficientList[Series[1/Sum[Round[(k + 1)*r] (-x)^k, {k, 0, z}], {x, 0, z}],
%t A289916 x]; (* A289916 *)
%t A289916 v = N[u[[z]]/u[[z - 1]], 200]
%t A289916 RealDigits[v, 10][[1]] (* A289917 *)
%o A289916 (PARI) Vec((1+x)^2*(1-x+x^2-x^3+x^4-x^5+x^6) / ((1-x+x^2)*(1-x-x^2-x^3+x^4)) + O(x^50)) \\ _Colin Barker_, Jul 20 2017
%Y A289916 Cf. A078140 (includes guide to related sequences), A289917.
%K A289916 nonn,easy
%O A289916 0,2
%A A289916 _Clark Kimberling_, Jul 18 2017